Optimal dynamic investment policy for different tax depreciation rates and economic depreciation rates
The authors analyze the investment policy of a firm in the case when a tax depreciation rate is different from the economic depreciation rate. Let \(K_1(t)\) denote the stock of productive capital at time \(t\) and let \(I(t)\) denote the gross investment rate at time \(t\). Then for the net investment we have the equation \(\dot K_1=I-\beta K_1,\;K_1(0)>0\), where \(\beta>0\) is the constant rate of technical depreciation. The evolution of the tax base \(K_2(t)\) is given by \(\dot K_2=I-\gamma K_2-[C(K_1)-\gamma K_2]^{-}\), where \(C(K_1)\) is the revenue, \(C(0)=0, C'(K_1)>0,C''(K_1)<0\), \(\gamma>0\) is the tax depreciation rate. Investments are assumed to be irreversible \(I\geq 0\) and dividend payments \(D(t)\) are restricted to be nonnegative: \(D=C(K_1)-T[C(K_1)-\gamma K_2]^{+}-I\geq 0\), where \(T>0\) is the fixed tax rate. Let \(r>0\) be the constant discount rate, then the objective of the firm can be expressed by \[ \max_{I}\int_0^{z}D(t)e^{-rt} dt+ [(1-T)/r]C(K_1(z))+[\gamma\beta T/(r(r+\gamma))-\beta/r]K_1(z)+ [\gamma/(r+\gamma)]TK_2(z), \] where \(z\) is the horizon date.
scientific article; zbMATH DE number 1533378